DOI QR코드

DOI QR Code

The influence of initial stress on wave propagation and dynamic elastic coefficients

  • Li, Xibing (School of Resources and Safety Engineering, Central South University) ;
  • Tao, Ming (School of Resources and Safety Engineering, Central South University)
  • Received : 2014.09.12
  • Accepted : 2014.12.10
  • Published : 2015.03.25

Abstract

The governing equations of wave propagation in one dimension of elastic continuum materials are investigated by taking the influence of the initial stress into account. After a short review of the theory of elastic wave propagation in a rock mass with an initial stress, results indicate that the initial stress differentially influences P-wave and S-wave propagation. For example, when the initial stress is homogeneous, for the P-wave, the initial stress only affects the magnitude of the elastic coefficients, but for the S-wave, the initial stress not only influences the elastic coefficients but also changes the governing equation of wave propagation. In addition, the P-wave and S-wave velocities were measured for granite samples at a low initial stress state; the results indicate that the seismic velocities increase with the initial stress. The analysis of the previous data of seismic velocities and elastic coefficients in rocks under ultra-high hydrostatic initial stress are also investigated.

Keywords

Acknowledgement

Supported by : National Natural Science Foundation of China

References

  1. Asef, M.R. and Najibi, A.R. (2013), "The effect of confining pressure on elastic wave velocities and dynamic to static Young's modulus ratio", Geophysics, 78(3), D135-D142. https://doi.org/10.1190/geo2012-0279.1
  2. Biot, M.A. (1964), Mechanics of Incremental Deformations, Wiley, New York, NY, USA.
  3. Birch, F. (1960), "The velocity of compressional waves in rocks to 10 kilobars, part 1", J Geophys. Res., 65(4), 1083-1102. https://doi.org/10.1029/JZ065i004p01083
  4. Birch, F. (1961), "The velocity of compressional waves in rocks to 10 kilobars: 2", J. Geophys. Res., 66(7), 2199-2224. https://doi.org/10.1029/JZ066i007p02199
  5. Brady, B.H. (2004), Rock Mechanics: For Underground Mining, Springer Science & Business Media.
  6. Chevrot, S. and van der Hilst, R.D. (2000), "The poisson ratio of the Australian crust: Geological and geophysical implications", Earth Planetary Sci. Lett., 183(1), 121-132. https://doi.org/10.1016/S0012-821X(00)00264-8
  7. Christensen, N.I. (1965), "Compressional wave velocities in metamorphic rocks at pressures to 10 kilobars", J. Geophys. Res., 70(24), 6147-6164. https://doi.org/10.1029/JZ070i024p06147
  8. Christensen, N.I. (1974), "Compressional wave velocities in possible mantle rocks to pressures of 30 kilobars", J. Geophys. Res., 79(2), 407-412. https://doi.org/10.1029/JB079i002p00407
  9. Ji, S., Wang, Q. and Xia, B. (2002), Handbook of Seismic Properties of Minerals, Rocks and Ores, Polytechnique International Press, Montreal, QC, Canada.
  10. Ji, S., Wang, Q., Marcotte, D., Salisbury, M.H. and Xu, Z. (2007), "P-wave velocities, anisotropy and hysteresis in ultrahigh‐pressure metamorphic rocks as a function of confining pressure", J. Geophys. Res.: Solid Earth, 112(B9).
  11. Manghnani, M.H., Ramananantoandro, R. and Clark, S.P. (1974), "Compressional and shear wave velocities in granulite facies rocks and eclogites to 10 kbar', J. Geophys. Res., 79(35), 5427-5446. https://doi.org/10.1029/JB079i035p05427
  12. Ogden, R. and Sotiropoulos, D. (1995), "On interfacial waves in pre-stressed layered incompressible elastic solids", Proceedings of the Royal Society of London: Series A, Mathematical and Physical Sciences, 450(1939), pp. 319-341.
  13. Ogden, R. and Sotiropoulos, D. (1997), "The effect of pre-stress on the propagation and reflection of plane waves in incompressible elastic solids", IMA J. Appl. Math., 59(1), 95-121. https://doi.org/10.1093/imamat/59.1.95
  14. Shaocheng, J., Salisbury, M.H. and Hanmer, S. (1993), "Petrofabric, P-wave anisotropy and seismic reflectivity of high-grade tectonites", Tectonophysics, 222(2), 195-226. https://doi.org/10.1016/0040-1951(93)90049-P
  15. Sharma, M. and Garg, N. (2006), "Wave velocities in a pre-stressed anisotropic elastic medium", J. Earth Syst. Sci., 115(2), 257-265. https://doi.org/10.1007/BF02702040
  16. Sun, S., Ji, S., Wang, Q., Xu, Z., Salisbury, M. and Long, C. (2012), "Seismic velocities and anisotropy of core samples from the Chinese Continental Scientific Drilling borehole in the Sulu UHP terrane, Eastern China", J. Geophys. Res.: Solid Earth, 117(B1).
  17. Tao, M., Li, X. and Wu, C. (2013), "3D numerical model for dynamic loading-induced multiple fracture zones around underground cavity faces", Comput. Geotech., 54, 33-45. https://doi.org/10.1016/j.compgeo.2013.06.002
  18. Wang, Q. and Ji, S. (2009), "Poisson's ratios of crystalline rocks as a function of hydrostatic confining pressure", J. Geophys. Res.: Solid Earth, 114(B9).
  19. Wang, Q., Ji, S., Sun, S. and Marcotte, D. (2009), "Correlations between compressional and shear wave velocities and corresponding Poisson's ratios for some common rocks and sulfide ores", Tectonophysics, 469(1), 61-72. https://doi.org/10.1016/j.tecto.2009.01.025

Cited by

  1. Charts for estimating rock mass shear strength parameters vol.10, pp.3, 2016, https://doi.org/10.12989/gae.2016.10.3.257
  2. Theoretical and numerical analysis of the influence of initial stress gradient on wave propagations vol.10, pp.3, 2016, https://doi.org/10.12989/gae.2016.10.3.285
  3. Failure mechanism and coupled static-dynamic loading theory in deep hard rock mining: A review vol.9, pp.4, 2017, https://doi.org/10.1016/j.jrmge.2017.04.004
  4. Determination of spalling strength of rock by incident waveform vol.12, pp.1, 2015, https://doi.org/10.12989/gae.2017.12.1.001
  5. Comparative study on dynamic properties of argillaceous siltstone and its grouting-reinforced body vol.13, pp.2, 2015, https://doi.org/10.12989/gae.2017.13.2.333
  6. Behaviour of a plane joint under horizontal cyclic shear loading vol.13, pp.5, 2015, https://doi.org/10.12989/gae.2017.13.5.809
  7. On the elastic parameters of the strained media vol.67, pp.1, 2015, https://doi.org/10.12989/sem.2018.67.1.053
  8. Determination of elastic parameters of the deformable solid bodies with respect to the Earth model vol.15, pp.5, 2015, https://doi.org/10.12989/gae.2018.15.5.1071
  9. Theoretical Analysis of Longitudinal Wave Attenuation in a Stressed Rock With Variable Cross-Section vol.7, pp.None, 2015, https://doi.org/10.3389/feart.2019.00270
  10. Frictional responses of concrete-to-concrete bedding planes under complex loading conditions vol.17, pp.3, 2015, https://doi.org/10.12989/gae.2019.17.3.253
  11. Estimation of tensile strength of ultramafic rocks using indirect approaches vol.17, pp.3, 2015, https://doi.org/10.12989/gae.2019.17.3.261
  12. Dynamic response and failure of rock in initial gradient stress field under stress wave loading vol.27, pp.3, 2015, https://doi.org/10.1007/s11771-020-4344-8
  13. Determining the transverse isotropic rocks’ static elastic moduli with cylindrical plugs: Shortfalls, challenges, and expected outcomes vol.86, pp.3, 2015, https://doi.org/10.1190/geo2020-0439.1